# Energy of a complex exponential

I want to obtain the energy of this signal $$x_i(t)= e^{j2\pi(2i-1)f_0t}$$ where $$f_0 = 1$$ Hz, $$i= 1,...,4$$ and $$j$$ is a complex. I think I need to use the Fourier transform or the Parseval theorem but I'm not sure how to apply it.

• You can just take the squared magnitude and integrate it between to time bounds, and see what happen May 7 at 17:57

Notice that the magnitude of $$|e^{a+bj}| = |e^a||e^{bj}| = e^a$$ for $$a,b \in \mathbb{R}$$, comparing with your function we see that $$|x_i(t)|=1$$. We conclude that $$x_i(t)$$ is a power signal, not an energy signal, i.e. you must define a time interval to integrate. Then the energy will be $$\int_{t_0}^{t_f} |x_i(t)|^2 \mathrm{d}t = (t_f - t_0)$$. I hope this helps.
• Cleanly done. I just correcting the upright $\mathrm{d}$ May 7 at 18:38